Peer-to-peer (P2P) technology provides a scalable solution in multimedia streaming. Many streaming applications, such as IPTV and video conferencing, have rigorous constraints on end-to-end delays. Obtaining assurances on meeting those delay constraints in dynamic and heterogenous network environments is a challenge. In this paper, we devise a streaming scheme which minimizes the maximum end-to-end streaming delay for a mesh-based overlay network paradigm. We first formulate the minimum-delay P2P streaming problem, called the MDPS problem, and prove its NP-completeness. We then present a polynomialtime approximation algorithm to this problem, and show that the performance of our algorithm is bounded by a ratio of O( √ log n). Our simulation study reveals the effectiveness of our algorithm, and shows a reasonable message overhead.